There were doubts over whether the pair, who are both owned by Red Bull, would be able to compete in European club football's elite competition due to a potential violation of Article 5, which relates to the integrity of the competition.
They will move directly into the group stages, while Salzburg will meet either Hibernians or Tallinn in the second qualifying round.
"The Adjudicatory Chamber of the UEFA Club Financial Control Body (CFCB) has decided to accept the admission of both FC Salzburg and RB Leipzig to the UEFA Champions League 2017/18, having found that Article 5 (Integrity of the competition) of the competition regulations is not breached," an official statement reads.
"Following a thorough investigation, and further to several important governance and structural changes made by the clubs (regarding corporate matters, financing, personnel, sponsorship arrangements, etc.), the CFCB deemed that no individual or legal entity had anymore a decisive influence over more than one club participating in a UEFA club competition.
"This decision may be appealed to the Court of Arbitration for Sport within ten days, in accordance with Article 34(2) of the Procedural rules governing the UEFA Club Financial Control Body – Edition 2015, as well as Articles 62 and 63 of the UEFA Statutes.
"The CFCB will continue to monitor both clubs to ensure that integrity rules are respected going forward."